1. Field of the Invention
The present invention relates to a holographic-display apparatus, and more particularly to an apparatus for forming holographic three-dimensional (3-D) optical images corresponding to input object image information. Further, the present invention specifically relates to a computer-assisted holographic display system for calculating wave front (diffraction image) data obtained on the hologram plane based on sampling data of a 3-D object, calculating interference pattern data between the calculated diffraction pattern data and reference light data, and forming an interference pattern corresponding to the interference pattern data on a spatial light modulator such as a liquid crystal spatial light modulator. Further, the present invention specifically relates to a computer assisted holographic-display system for calculating wave front (diffraction image) data obtained on the hologram plane based on sampling data of a 3-D object, and forming a phase-modulation pattern corresponding to the calculated wave front data on a spatial light modulator such as a liquid crystal spatial light modulator.
2. Description of the Related Art
The computer holography is a technique for forming an optical image of a 3-D object on a plane medium (which is normally called "holographic plate") with the assistance of a highly advanced computer. With the recent development of the digital equipment, the computer hologram technique becomes increasingly important in the application field of 3-D image data process, measurement and display thereof, for example.
Unlike the existing purely optical hologram devices, the computer-hologram apparatus produces by computation a holographic image pattern to record a resultant computer-generated holographic image on a recording medium of selected type. Since the computer can create any desired 3-D object images including imaginary graphic images, the computer hologram is excellent in flexibility and wide in applicability for the industrial use. The presently available computer hologram apparatus, however, suffers from the fact that the efficiency of computation remains low. An increased amount of repetitive computations should be required to produce a computer hologram. The necessity of such repetitive computations forces the total processing time to increase, which necessitates the use of a large-scale computer system. This reduces the production efficiency of 3-D object hologram which is required to be recorded to maintain the high quality of a reproduced image.
Until today, several techniques have been proposed for reducing in amount the image information to be processed, thereby to attain an increased computation efficiency in the art of computer hologram. One of the techniques may be found in what is called the "Lohmann type" computer hologram apparatus as is well known among those skilled in the art. This computer hologram apparatus generates a hologram by computing the diffraction pattern of an object. The computation algorithm is described, for example, in "Precision Machine", Vol. 47, No. 12, Supplement, (Dec. 6, 1981) at pp. 101-105, wherein a computer-generated hologram is formed by (1) inputting an object data to the computer, (2) deriving the wave of an object on the hologram plane by computation of the diffraction image to produce a binary-coded recording pattern, (3) forming an original picture drawing, and (4) reducing the original picture by photographing (completion of the hologram).
To reduce the amount of information to be computed, a hologram is created by dividing the hologram plane into a large number of small picture points (called "cells"), computing a diffraction pattern at the representative point of each cell to derive the complex amplitude and phase of each point, and giving an opening to each cell according to the computation results. The opening given to each cell is determines as follows: the height of opening is determined in accordance with the computed value of the complex amplitude of a corresponding cell, whereas the positional relation (distance) between the center of the opening and the cell center is determined in accordance with the value of the phase. The method of determining the size and position of the opening for each cell is described in detail in A. W. Lohmann & D. P. Paris "Binary Fraunhofer Holograms generated by Computer" Appl. Oct., Vol. 6, No. 10 (October 1967) at pp. 1739-1748. An original object image can be optically reconstructed or reproduced by applying a coherent reconstructing light such as laser light to the recorded hologram. A resultant reproduced image obtained from the computer hologram, however, is not satisfactory in the image quality. This is because the center of the cell opening is positionally deviated from the representative point used as the basis for computations of phase.
Another method of forming a computer hologram is also known which is based on the computation of a fringe-shaped interference pattern. The interference computation type computer-generated holography is conceptually similar to a conventional optical hologram forming scheme in that a reference light emitted from a laser source is superposed on the diffraction image of an object of interest to derive an interference pattern therebetween. The recording of a hologram is performed so that the transmissivity or the density may vary on a photographic plate in accordance with the intensity of a resulting fringe-like interference pattern.
According to the interference computation type computer-generated holography, unlike the aforementioned diffraction computation type (i.e., Lohmann type) computer-generated holography, the phase information of a holographic image is recorded in the interference fringe form. The phase error can thus be minimized, which leads to enhancement of the image quality. However, the interference computation type holography suffers from the decreased computation efficiency due to the fact that the decisive means for reducing the amount of information used to compute the interference pattern has not been accomplished yet. Extra large-capacity semiconductor memories are necessary to execute the computation for an enormous amount of information. This results in that the scale of the hologram recording system is increased unwantedly, which makes almost impossible the accomplishment of a high-speed computation process with the use of a smaller computer system. This is a serious bar to the industrial spread of the computer hologram recording system.
Further, as a method for creation of the computer hologram, a method (Kinoform) for deriving phase data of the diffraction wave of an object and directly recording the data on a phase modulation type medium is known. In the hologram of a type which is based on the diffraction wave of the object as described above, since the spatial frequency of information to be calculated can be made lower than that of the interference fringe type, the amount of information to be processed or the amount of calculations can be reduced. However, even in this case, since a relatively large amount of error components of the wave front may remain if the light modulation is effected by use of a less amount of information, unnecessary diffraction light will occur, thereby causing a problem that an image to be displayed becomes dark or the quality of the image is lowered. In order to solve the above problem, it is necessary to increase an amount of information to be processed and effect a large amount of calculations, and as a result, it becomes difficult to construct a practical system.